System and method for i-q imbalance correction

ABSTRACT

Systems and methods are disclosed for compensating I-Q imbalance in a wireless receiver. The receiver may employ a quadrature downconverter configured to receive an RF signal input and output an in-phase component and a quadrature component at an IF, an IF rotation block configured to downconvert the in-phase and quadrature components to baseband and an I-Q correction block configured to compensate for an I-Q imbalance in the received signal, wherein the I-Q correction block is positioned downstream from the IF rotation block in the signal path. Performing the I-Q correction after conversion to baseband may allow the compensation calculations to operate at a reduced digital rate. Similarly, digitally adjusting the gain of the signal prior to I-Q compensation may reduce the number of bits that are manipulated during the compensation process. These features may represent significant efficiencies as compared to I-Q corrections performed at IF.

FIELD OF THE PRESENT INVENTION

This disclosure generally relates to digital intermediate frequencyreceivers and more particularly to techniques for correcting I-Qimbalance to provide enhanced image rejection.

BACKGROUND OF THE INVENTION

Radio frequency (RF) communication systems generally rely on theupconversion of a data signal to a suitable carrier frequency fortransmission and then downconversion at the receiver. One populararchitecture for wireless receivers is a superheterodyne design in whichthe frequency downconversion takes place in at least two stages. Thereceived signal may first be downconverted from the carrier frequency toan intermediate frequency (IF). Downconversion to IF from the carrierfrequency facilitates filtering and amplifying the signal by the frontend of the receiver. Subsequently, the IF signal may then bedownconverted to baseband to allow recovery of the data signal.

While IF receivers exhibit a number of desirable attributes, theytypically require an image rejection strategy to compensate for thegeneration of the image frequency that results from the downconversionto IF. Receivers employing a quadrature architecture provide imagerejection through the use of two distinct channels to form the in-phase(I) and the quadrature-phase (Q) components of the received signal.Through appropriate filtering and mixing of the I and Q components,image rejection of interfering jammers may be achieved. A quadraturegenerator mixes the sine and cosine components of the carrier signal toextract the I and Q components. As will be appreciated, if the twosignal components have a phase relationship of 90° with respect to oneanother, the interfering image may be perfectly rejected.

In practice, the quadrature generator uses the signal output by a localoscillator that does not perform in an ideal manner. As a result, thegenerated I and Q signal components may have phases that are not exactly90° with respect to each other or the signal components may experiencedifferent gains. Therefore, as used herein, the term I-Q imbalanceincludes phase mismatch, unequal gain, or both. Notably, any I-Qimbalance may result in imperfect cancellation of the interfering image.Consequently, many strategies have been implemented to correct for I-Qimbalance to improve image rejection.

Conventional approaches may involve applying a correction at IF tocompensate for the I-Q imbalance. For example, FIG. 1 depicts asimplified block diagram of a prior art digital receiver 100. As shown,an RF signal is received at antenna 102 and fed through low noiseamplifier (LNA) 104 to quadrature downconverter 106, which mixes cosineand sine signals at the carrier frequency from local oscillator 108 togenerate the in-phase (I) and quadrature (Q) signal components. Eachchannel includes lowpass filters 110 and 112 and analog to digitalconverters (ADCs) 114 and 116, respectively, and provides the digitizedcomponents to digital signal processor (DSP) 120. Within DSP 120, the Iand Q signal components are combined by adder 122, fed through filters124 and input to I-Q correction block 126. The corrected signal isdownconverted to baseband by IF rotation block 128 by mixing with outputfrom a local oscillator (LO) 130, fed through filters 132, and gainadjusted by digital variable gain amplifier (DVGA) 134. Decimator 136then reduces the sample rate of the signal and outputs to demodulator138 to recover the data stream.

As will be appreciated, the I-Q correction provided by receiver 100involves performing the calculations necessary to compensate for any I-Qimbalance to the signal at IF. Consequently, receiver 100 performs thecorrection at the digital sample rate of the IF signal and prior to gainadjustment by DVGA 134. Performing the I-Q imbalance correction in thismanner may require considerable computational resources and powerexpenditure. Accordingly, the techniques of this disclosure are directedto providing I-Q imbalance correction with reduced power consumption andcomputational overhead.

SUMMARY OF THE INVENTION

In accordance with the above needs and those that will be mentioned andwill become apparent below, this specification discloses a digitalwireless receiver for receiving a data signal, wherein the receiver hasa signal path including a quadrature downconverter configured to receivea radio frequency (RF) signal corresponding to the data signal andoutput an in-phase component and a quadrature component at anintermediate frequency (IF), an IF rotation block configured todownconvert the in-phase component and quadrature component to basebandand an I-Q correction block configured to compensate for an I-Qimbalance in the received signal, wherein the I-Q correction block ispositioned downstream from the IF rotation block in the signal path.

In one aspect, the receiver further may include a digital variable gainelement positioned upstream from the I-Q correction block in the signalpath. In another aspect, the receiver may include analog to digitalconverters operating at a sample rate to digitize the in-phase componentand the quadrature component produced by the quadrature downconverterand a decimator configured to provide an internal rate lower than thesample rate, wherein the I-Q correction block is positioned downstreamfrom the decimator in the signal path. In yet another aspect, thereceiver includes both the digital variable gain element and thedecimator. Accordingly, the I-Q correction block may operate at theinternal rate.

Further, upconversion of the data signal to IF prior to transmission maybe modeled by a matrix A such that IF rotation block may be configuredto perform an operation corresponding to multiplication by an inverse ofmatrix A, matrix A⁻¹. In addition, the I-Q imbalance may be modeled as amatrix B such that the I-Q correction block may be configured to performa matrix multiplication by A⁻¹B⁻¹A.

$\begin{bmatrix}c_{11} & c_{12} \\c_{21} & c_{22}\end{bmatrix},$

In such embodiments, A⁻¹B⁻¹A may equal where

$c_{11} = {{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} - {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{{\alpha cos}(\theta)}}$$c_{12} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + {{\tan (\theta)}{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{21} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} - {{\tan (\theta)}{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{22} = {{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} + {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$

T_(in) is an internal digital rate of the receiver and f_(IF) is the IF.

The receiver may also include a look up table holding values for c₁₁,c₁₂, c₂₁ and c₂₂. As desired, the values for the look up table may bedetermined during calibration.

This disclosure is also directed to a method for providing I-Q imbalancecompensation for a received data signal including the steps of mixing areceived RF signal corresponding to the data signal with a cosine outputof a local oscillator to extract an in-phase component at IF and a sineoutput of the local oscillator to extract a quadrature component at IF,applying an IF rotation to the in-phase component and the quadraturecomponent to downconvert the in-phase component and the quadraturecomponent to baseband, and applying an I-Q imbalance compensation to thein-phase component and the quadrature component at baseband.

Notably, the method may include digitally adjusting the gain of thein-phase component and the quadrature component prior to applying theI-Q imbalance compensation. Further, the method may include downsamplingthe sample rate of the in-phase component and the quadrature componentat IF to an internal rate lower than the sample rate prior to applyingthe I-Q imbalance compensation. As desired, both steps may be employed.In addition, the I-Q imbalance compensation may be applied at theinternal rate.

In one aspect, upconversion of the data signal to IF prior totransmission is modeled by a matrix A such that applying the IF rotationto the in-phase component and the quadrature component corresponds tomultiplication by an inverse of matrix A, matrix A⁻¹. Further, the I-Qimbalance may be modeled as a matrix B such that applying the I-Qimbalance compensation to the in-phase component and the quadraturecomponent at baseband corresponds to matrix multiplication by A⁻¹B⁻¹A.

In one embodiment,

${{A^{- 1}B^{- 1}A} = \begin{bmatrix}c_{11} & c_{12} \\c_{21} & c_{22}\end{bmatrix}},$

where

$c_{11} = {{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} - {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$$c_{12} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + {{\tan (\theta)}{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{21} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} - {{\tan (\theta)}{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{22} = {{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} + {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$

T_(in) is an internal digital rate of the receiver and f_(IF) is the IF.

In a further aspect, the method may include storing values for c₁₁, c₁₂,c₂₁ and c₂₂ in a look up table. The method may also include determiningthe values for the look up table during calibration.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages will become apparent from the followingand more particular description of the preferred embodiments of theinvention, as illustrated in the accompanying drawings, and in whichlike referenced characters generally refer to the same parts or elementsthroughout the views, and in which:

FIG. 1 depicts a prior art receiver architecture for providing I-Qimbalance compensation;

FIG. 2 schematically depicts upconversion of a data-bearing signal toIF, that may be used with an embodiment of the invention;

FIG. 3 schematically depicts quadrature downconversion of a data-bearingsignal to in-phase and quadrature components subject to I-Q imbalances,that may be used with an embodiment of the invention;

FIG. 4 schematically depicts a matrix model of a data-bearing signaloutput by the front end of a receiver, that may be used with anembodiment of the invention;

FIG. 5 schematically depicts a matrix model for conventional I-Qimbalance compensation;

FIG. 6 schematically depicts the equalization architecture forconventional I-Q imbalance compensation;

FIG. 7 depicts an exemplary receiver architecture for providing I-Qimbalance compensation, according to an embodiment of the invention; and

FIG. 8 schematically depicts a matrix model for I-Q imbalancecompensation, according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

At the outset, it is to be understood that this disclosure is notlimited to particularly exemplified materials, architectures, routines,methods or structures as such may, of course, vary. Thus, although anumber of such options, similar or equivalent to those described herein,can be used in the practice or embodiments of this disclosure, thepreferred materials and methods are described herein.

It is also to be understood that the terminology used herein is for thepurpose of describing particular embodiments of this disclosure only andis not intended to be limiting.

The detailed description set forth below in connection with the appendeddrawings is intended as a description of exemplary embodiments of thepresent invention and is not intended to represent the only exemplaryembodiments in which the present invention can be practiced. The term“exemplary” used throughout this description means “serving as anexample, instance, or illustration,” and should not necessarily beconstrued as preferred or advantageous over other exemplary embodiments.The detailed description includes specific details for the purpose ofproviding a thorough understanding of the exemplary embodiments of thespecification. It will be apparent to those skilled in the art that theexemplary embodiments of the specification may be practiced withoutthese specific details. In some instances, well known structures anddevices are shown in block diagram form in order to avoid obscuring thenovelty of the exemplary embodiments presented herein.

For purposes of convenience and clarity only, directional terms, such astop, bottom, left, right, up, down, over, above, below, beneath, rear,back, and front, may be used with respect to the accompanying drawingsor chip embodiments. These and similar directional terms should not beconstrued to limit the scope of the invention in any manner.

In this specification and in the claims, it will be understood that whenan element is referred to as being “connected to” or “coupled to”another element, it can be directly connected or coupled to the otherelement or intervening elements may be present. In contrast, when anelement is referred to as being “directly connected to” or “directlycoupled to” another element, there are no intervening elements present.

“Complementary logic,” which refers to logic circuitry involving bothP-channel and N-channel transistors, is often more commonly referred toas CMOS (Complementary Metal Oxide Semiconductor) logic even though thetransistors making up the logic circuitry may not have metal gates andmay not have oxide gate dielectrics.

The terms second level and first level, high and low and 1 and 0, asused in the following description may be used to describe various logicstates as known in the art. Particular voltage values of the second andfirst levels are defined arbitrarily with regard to individual circuits.Furthermore, the voltage values of the second and first levels may bedefined differently for individual signals such as a clock and a digitaldata signal. Although specific circuitry has been set forth, it will beappreciated by those skilled in the art that not all of the disclosedcircuitry is required to practice the invention. Moreover, certain wellknown circuits have not been described, to maintain focus on theinvention. Similarly, although the description refers to logical “0” andlogical “1” or low and high in certain locations, one skilled in the artappreciates that the logical values can be switched, with the remainderof the circuit adjusted accordingly, without affecting operation of thepresent invention.

Some portions of the detailed descriptions which follow are presented interms of procedures, logic blocks, processing and other symbolicrepresentations of operations on data bits within a computer memory.These descriptions and representations are the means used by thoseskilled in the data processing arts to most effectively convey thesubstance of their work to others skilled in the art. In the presentapplication, a procedure, logic block, process, or the like, isconceived to be a self-consistent sequence of steps or instructionsleading to a desired result. The steps are those requiring physicalmanipulations of physical quantities. Usually, although not necessarily,these quantities take the form of electrical or magnetic signals capableof being stored, transferred, combined, compared, and otherwisemanipulated in a computer system.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meaning as commonly understood by one having ordinaryskill in the art to which the disclosure pertains.

Further, all publications, patents and patent applications cited herein,whether supra or infra, are hereby incorporated by reference in theirentirety.

Finally, as used in this specification and the appended claims, thesingular forms “a, “an” and “the” include plural referents unless thecontent clearly dictates otherwise.

As will be discussed in detail below, this disclosure is directed to areceiver for use in a wireless communication system, wherein thereceiver has a signal path comprising a quadrature downconverterconfigured to receive an RF signal input and output, an in-phasecomponent and a quadrature component at an IF, an IF rotation blockconfigured to downconvert the in-phase and quadrature components tobaseband and an I-Q correction block configured to compensate for an I-Qimbalance in the received signal, wherein the I-Q correction block ispositioned downstream from the IF rotation block in the signal path.These techniques may be applied to any suitable digital heterodyne-basedreceiver, including those used in wireless communications systems suchas BLUETOOTH® (Bluetooth), wireless local area networks (WLANs) based onIEEE 802.11 protocols, and the like.

As discussed above, inaccuracies in the local oscillator of a receivermay introduce an I-Q imbalance in the modulated signal at the IF. Amatrix model may be used to estimate the I-Q imbalance and tosubsequently compensate for the imbalance through the use of a suitablyconfigured I-Q correction block. A real data passband signal with an IFmay be expressed as Equation (1):

s _(p)(t)=√{square root over (2)}x ₁(t)cos 2π(f _(c) +f _(IF))t−√{squareroot over (2)}x _(Q)(t)sin 2π(f _(c) +f _(IF))t,

where x_(l)(t) and x_(Q)(t) are the I and Q components of the datasignal, respectively, f_(c) is the carrier frequency and f_(IF) is theIF. Further, the real passband signal may also be represented usingcomplex baseband analysis as Equation (2):

s _(p)(t)=

e{√{square root over (2)}w _(bb)(t)e ^(j2πf) ^(t)},

where w_(bb)(t) is the equivalent complex baseband signal of the signals_(p)(t) and is given by Equation (3):

$\begin{matrix}\begin{matrix}{{w_{bb}(t)} = {{s_{bb}(t)}^{{j2\pi}\; f_{IF}t}}} \\{= {\left( {{x_{I}(t)} + {j\; {x_{Q}(t)}}} \right)^{j\; 2\pi \; f_{IF}t}}} \\{= {\left( {{{x_{I}(t)}{\cos \left( {2\pi \; f_{IF}t} \right)}} - {{x_{Q}(t)}{\sin \left( {2\pi \; f_{IF}t} \right)}}} \right) +}} \\{{j\left( {{{x_{I}(t)}{\sin \left( {2\pi \; f_{IF}t} \right)}} + {{x_{Q}(t)}{\cos \left( {2\pi \; f_{IF}t} \right)}}} \right)}}\end{matrix} & (3)\end{matrix}$

where w_(bb)(t)=x₁(t)+jx_(Q)(t) is the data-bearing signal. FromEquations (2) and (3), w_(bb)(t) for the IF receiver may be expressed inthe form of a matrix product as indicated in Equation (6):

$\begin{matrix}{{\begin{bmatrix}{\cos \left( {2\pi \; f_{IF}t} \right)} & {- {\sin \left( {2\pi \; f_{IF}t} \right)}} \\{\sin \left( {2\pi \; f_{IF}t} \right)} & {\cos \left( {2\pi \; f_{IF}t} \right)}\end{bmatrix}\begin{bmatrix}{x_{I}(t)} \\{x_{Q}(t)}\end{bmatrix}} = \begin{bmatrix}{\Re \; e\left\{ {w_{bb}(t)} \right\}} \\{{Im}\left\{ {w_{bb}(t)} \right\}}\end{bmatrix}} & (4)\end{matrix}$

One of skill in the art will appreciate that Equation (6) corresponds tothe upconversion to IF of the data-bearing signal as shown schematicallyin FIG. 2. Accordingly, for the purposes of this disclosure, matrix Amay be defined as

$\quad\begin{bmatrix}{\cos \left( {2\pi \; f_{IF}t} \right)} & {- {\sin \left( {2\pi \; f_{IF}t} \right)}} \\{\sin \left( {2\pi \; f_{IF}t} \right)} & {\cos \left( {2\pi \; f_{IF}t} \right)}\end{bmatrix}$

and represents the upconversion of the data-bearing signal.

As described above, the passband signal at the receiver is downconvertedto IF and the I and Q components extracted by a quadrature downconverterthat mixes the cosine and sine components of a signal generated by alocal oscillator. Due to performance of the local oscillator, the I andQ signals may not have the 90° phase relationship with each other andmay have unequal gain, leading to phase mismatch and gain imbalancebetween the two components. By establishing the I signal component asthe reference, the gain imbalance α and phase mismatch θ may beexpressed with regard to the Q signal component as indicated by Equation(7):

s ₁(t)=x ₁(t)

s _(Q)(t)=αsin(θ)x ₁(t)+αcos(θ)x _(Q)(t)  (7)

Accordingly, when there is no I-Q imbalance such that α=1 and θ=0,s_(Q)(t)=x_(Q)(t) indicates the receiver correctly detects the desiredcomponents.

FIG. 3 schematically depicts the quadrature downconversion of thepassband data-bearing signal using a local oscillator having gainimbalance and phase mismatch in the analog front end of receiver. Asshown, the I and Q signal components are filtered and digitized toprovide the IF signal components, s₁[n] and s_(Q)[n]. In view of thecomplex baseband signal w_(bb)(t) defined in Equation (3), the I-Qimbalance may also be modeled as a matrix product, as indicated byEquation (8):

$\begin{matrix}{\begin{bmatrix}{s_{I}(t)} \\{s_{Q}(t)}\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{{\alpha sin}(\theta)} & {{\alpha cos}(\theta)}\end{bmatrix}\begin{bmatrix}{\Re \; e\left\{ {w_{bb}(t)} \right\}} \\{{Im}\left\{ {w_{bb}(t)} \right\}}\end{bmatrix}}} & (8)\end{matrix}$

In turn, for the purposes of this disclosure, matrix B may be defined as

$\quad\begin{bmatrix}1 & 0 \\{{\alpha sin}(\theta)} & {{\alpha cos}(\theta)}\end{bmatrix}$

and represents the effect of I-Q imbalance on the data-bearing signal.

The above discussion establishes that the signal produced by the frontend of a quadrature receiver may be modeled as a product resulting frommultiplication of the signal by the two matrices, A and B, as shown inFIG. 4. Returning to the example of conventional receiver 100 depictedin FIG. 1, a strategy for correcting the I-Q imbalance may involveperforming matrix inversions using the matrices B⁻¹ and A⁻¹ on the frontend output of receiver 100, as schematically represented in FIG. 5,wherein

$B^{- 1} = {{\frac{1}{\alpha \; {\cos (\theta)}}\begin{bmatrix}{\alpha \; {\cos (\theta)}} & 0 \\{- {{\alpha sin}(\theta)}} & 1\end{bmatrix}} = {\begin{bmatrix}1 & 0 \\{- {\tan (\theta)}} & {1/\left\lbrack {{\alpha cos}(\theta)} \right\rbrack}\end{bmatrix}\mspace{14mu} {and}}}$ $A^{- 1} = {\begin{bmatrix}{\cos \left( {2\pi \; f_{IF}n\; T} \right)} & {\sin \left( {2\pi \; f_{IF}n\; T} \right)} \\{- {\sin \left( {2\pi \; f_{IF}n\; T} \right)}} & {\cos \left( {2\pi \; f_{IF}n\; T} \right)}\end{bmatrix}.}$

The sampling frequency of ADCs 114 and 116 is given by f_(s) andcorrespondingly, T is the sampling period 1/f_(s). Since matrix A⁻¹represents the downconversion by −f_(IF) performed by IF rotation block128, the conventional equalization architecture of receiver 100 may bedepicted schematically as shown in FIG. 6.

In particular, I-Q correction block 126 may be configured to perform acorrection corresponding to multiplying the digitized I and Q signal bythe inverse matrix B⁻¹ to compensate for the I-Q imbalance imparted by aquadrature downconverter. Following I-Q correction block 126 in thesignal path of receiver 100, IF rotation block 128 downconverts the IFsignal to baseband. This corresponds to multiplying the signal with theinverse matrix A⁻¹. The success of this strategy depends upon applyingthe compensation for I-Q imbalance using I-Q correction block 126 priorto IF rotation block 128 to preserve the order of operation such thatthe signal is multiplied by matrix B⁻¹ prior to being multiplied bymatrix A⁻¹.

In contrast, the techniques of this disclosure are directed to applyingcompensation for I-Q imbalance after the signal has been converted tobaseband. By positioning the I-Q correction block downstream from the IFrotation block, a number of efficiencies may be realized. In one aspect,a digital receiver may employ different data rates in different portionsof the circuitry. For example, the processing of the IF signal may takeplace at a higher digital rate than processing of the baseband signal.Correspondingly, positioning the I-Q correction block after the IFrotation allows the computations associated with compensating the I-Qimbalance to be performed at a lower digital rate. This reduced rateallows for reductions in circuitry area, cost and power consumption. Inanother aspect, positioning the I-Q correction block downstream from theIF rotation block also allows the compensation to be performed afteroperation of the DVGA. The role of the DVGA is to digitally scale theincoming signal such that it fits within an optimal bit width, so thesignal output from the DVGA may represent only the bits necessary forproper demodulation. Accordingly, compensating the I-Q imbalance afterdigital gain adjustment by the DVGA may reduce the complexity of theassociated calculations, also saving area, cost and power.

The matrices A and B used to model upconversion and I-Q imbalance do notexhibit the commutative property, so proper compensation may not beachieved by performing matrix multiplication with matrix B⁻¹ subsequentto multiplication with matrix A⁻¹. Rather, it may be seen that toprovide proper correction, a new matrix C may be defined, such thatC=A⁻¹B⁻¹A. By substituting the values for the matrices as given above,matrix C may be represented by Equation (9):

$\begin{matrix}{C = {{\begin{bmatrix}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)} & {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)} \\{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} & {\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}\end{bmatrix}\begin{bmatrix}1 & 0 \\{- {\tan (\theta)}} & {1/\left\lbrack {{\alpha cos}(\theta)} \right\rbrack}\end{bmatrix}}{\quad\begin{bmatrix}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)} & {- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} \\{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)} & {\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}\end{bmatrix}}}} & (5)\end{matrix}$

Performing the indicated multiplication results in matrix

${C = \begin{bmatrix}c_{11} & c_{12} \\c_{21} & c_{22}\end{bmatrix}},$

where

$c_{11} = {{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} - {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$$c_{12} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + {{\tan (\theta)}{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{21} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} - {{\tan (\theta)}{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{22} = {{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} + {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$

An example architecture for performing I-Q imbalance correction usingmatrix C is depicted in FIG. 7 with regard to digital receiver 700. Asshown, antenna 702 receives the RF signal which is then fed through lownoise amplifier (LNA) 704 to quadrature downconverter 706, which mixescosine and sine signals at the carrier frequency from local oscillator(LO) 708 to generate the in-phase (I) and quadrature (Q) signalcomponents. Each channel includes lowpass filters 710 and 712 and analogto digital converters (ADCs) 714 and 716, respectively, and provides thedigitized components to digital signal processor (DSP) 720. Within DSP720, the I and Q signal components are combined by adder 722, fedthrough filters 724 and downconverted to baseband by IF rotation block726 by mixing with output from LO 728. The baseband signal is then fedthrough filters 730 and gain adjusted by DVGA 732. I-Q correction block736 receives the output from decimator 734 and performs an I-Q imbalancecompensation corresponding to the multiplication of the signal by matrixC. The corrected signal is the sent to demodulator 738 to recover thedata stream. The functional architecture of receiver 700 isschematically depicted in FIG. 8. As shown, IF rotation block 726downconverts the signal to baseband, effectively applying multiplicationby matrix A⁻¹. After the reduction in digital rate by sampler 734, I-Qcorrection block 736 performs compensation corresponding tomultiplication by matrix C.

As described above, baseband portions of DSP 720 may operate at adifferent digital rate than IF portions, such that decimator 734 may beconfigured to reduce the sample rate of the signal by a desired factor.For example, the sample rate f_(s) of ADCs 714 and 716 may be 32 MHz. Byapplying a downsampling factor of 4, decimator 734 may output the signalat an internal rate f_(in) of 8 MHz. Accordingly, I-Q correction block736 may similarly operate at 8 MHz, representing substantial power andcircuitry savings with respect to prior art implementations that must beapplied to the IF signal and correspondingly operate at the sample rate.In general, the downsampling factor may be selected as desired whilepreferably maintaining the Nyquist sampling requirement. Further, sinceDVGA 732 reduces any unnecessary bits from the signal stream, thecomputational demand placed on I-Q correction block 736 is reduced,representing additional efficiencies.

I-Q correction block 736 may be configured to perform the multiplicationby matrix C in any suitable manner. In particular, a look up table (LUT)may be provided to store the possible values for gain (α) and phase (θ)mismatch. Further, an additional LUT may be employed to store the valuesfor the cosine and sine functions since the matrix C is a time-variantmatrix. Computation of the matrix C matrix values may be performed bysoftware during, for example, a calibration stage at power-on orcalculated dynamically for every sample, or by hardware. As will beappreciated, the choice is within the discretion of the system designerand may reflect computational resources available, desired performanceand other similar factors. In one example, receiver 700 may operate atan IF, f_(IF) of 727.27 MHz (32 MHz/44.) The number of values mnecessary to populate the LUT with entries for the functions may begiven by the ratio of the internal digital rate to the IF,f_(in)/f_(IF). As such, in receiver 700 operating with f_(in) of 8 MHz,m may equal 8/0.72727 or 11. Therefore, the resources associated withproviding the cosine and sine functions may be relatively modest.

Described herein are presently preferred embodiments. However, oneskilled in the art that pertains to the present invention willunderstand that the principles of this disclosure can be extended easilywith appropriate modification.

1. A digital wireless receiver for receiving a data signal, wherein thereceiver has a signal path comprising a quadrature downconverterconfigured to receive a radio frequency (RF) signal corresponding to thedata signal and output an in-phase component and a quadrature componentat an intermediate frequency (IF), an IF rotation block configured todownconvert the in-phase component and quadrature component to basebandand an in-phase (I)—quadrature (Q) correction block configured tocompensate for a modeled I-Q imbalance in the received signal, whereinthe I-Q correction block is positioned downstream from the IF rotationblock in the signal path.
 2. The receiver of claim I, wherein thereceiver further comprises a digital variable gain element positionedupstream from the I-Q correction block in the signal path.
 3. Thereceiver of claim 1, wherein the receiver further comprises analog todigital converters operating at a sample rate to digitize the in-phasecomponent and the quadrature component produced by the quadraturedownconverter and a decimator configured to provide an internal ratelower than the sample rate, wherein the I-Q correction block ispositioned downstream from the decimator in the signal path.
 4. Thereceiver of claim 3 wherein the receiver further comprises a digitalvariable gain element positioned upstream from the I-Q correction blockin the signal path.
 5. The receiver of claim 3, wherein the I-Qcorrection block operates at the internal rate.
 6. The receiver of claimI, wherein upconversion of the data signal to IF prior to transmissionis modeled by a matrix A and wherein the IF rotation block is configuredto perform an operation corresponding to multiplication by an inverse ofmatrix A, matrix A⁻¹.
 7. The receiver of claim 6, wherein the I-Qimbalance is modeled as a matrix B and wherein the I-Q correction blockis configured to perform a matrix multiplication by A⁻¹B⁻¹A.
 8. Thereceiver of claim 7, wherein ${{A^{- 1}B^{- 1}A} = \begin{bmatrix}c_{11} & c_{12} \\c_{21} & c_{22}\end{bmatrix}},$ where$c_{11} = {{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} - {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$$c_{12} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + {{\tan (\theta)}{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{21} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} - {{\tan (\theta)}{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{22} = {{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} + {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$T_(in) is an internal digital rate of the receiver and f_(IF) is the IF.9. The receiver of claim 8, further comprising a look up table holdingvalues for c₁₁, c₁₂, c₂₁ and c₂₂.
 10. The receiver of claim 9, whereinthe values for the look up table are determined during calibration. 11.A method for providing in-phase (I) quadrature (Q) imbalancecompensation for a received data signal, comprising: mixing a receivedradio frequency (RF) signal corresponding to the data signal with acosine output of a local oscillator to extract an in-phase component atintermediate frequency (IF) and a sine output of the local oscillator toextract a quadrature component at IF; applying an IF rotation to thein-phase component and the quadrature component to downconvert thein-phase component and the quadrature component to baseband; andapplying a modeled I-Q imbalance compensation to the in-phase componentand the quadrature component at baseband.
 12. The method of claim 11,further comprising digitally adjusting the gain of the in-phasecomponent and the quadrature component prior to applying the I-Qimbalance compensation.
 13. The method of claim 11, further comprisingdownsampling the sample rate of the in-phase component and thequadrature component at IF to an internal rate lower than the samplerate prior to applying the I-Q imbalance compensation.
 14. The method ofclaim 13 further comprising digitally adjusting the gain of the in-phasecomponent and the quadrature component prior to applying the I-Qimbalance compensation.
 15. The method of claim 13, wherein the I-Qimbalance compensation is applied at the internal rate.
 16. The methodof claim 11, wherein upconversion of the data signal to IF prior totransmission is modeled by a matrix A and wherein applying the IFrotation to the in-phase component and the quadrature componentcorresponds to multiplication by an inverse of matrix A, matrix A⁻¹. 17.The method of claim 16, wherein the I-Q imbalance is modeled as a matrixB and wherein applying the I-Q imbalance compensation to the in-phasecomponent and the quadrature component at baseband corresponds to matrixmultiplication by A⁻¹B⁻¹A.
 18. The method of claim 17, wherein where${{A^{- 1}B^{- 1}A} = \begin{bmatrix}c_{11} & c_{12} \\c_{21} & c_{22}\end{bmatrix}},$ where$c_{11} = {{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} - {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$$c_{12} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + {{\tan (\theta)}{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{21} = {{{- {\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} - {{\tan (\theta)}{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}}{\alpha \; {\cos (\theta)}}}$$c_{22} = {{\sin^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)} + {{\tan (\theta)}{\sin \left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\cos \left( {2\pi \; f_{IF}n\; T_{in}} \right)}} + \frac{\cos^{2}\left( {2\pi \; f_{IF}n\; T_{in}} \right)}{\alpha \; {\cos (\theta)}}}$T_(in) is an internal digital rate of the receiver and f_(IF) is the IF.19. The method of claim 18, further comprising storing values for c₁₁,c₁₂, c₂₁ and c₂₂ in a look up table.
 20. The method of claim 19, furthercomprising determining the values for the look up table duringcalibration.